WASHINGTON—The Federal Reserve should toughen banks’ capital requirements to reduce the risks of a credit crunch in the next downturn, Boston Fed President Eric Rosengren said in an interview Wednesday.

He said the Fed should start requiring banks to increase their levels of loss-absorbing capital, using a rule known as the countercyclical capital buffer. Raising the requirement, currently set at zero, would force banks to boost their capacity to absorb losses during good times, so they are less likely to pull back from lending...